Equation of states uses the ideal gas eqns. and describe and governs according to the physical conditions of parameters provided. And thus works accordingly to the laws like Boyles law , charles law...

We know that a meter bridge follows the Wheatstone Bridge principle that is P/Q=R/S For the first part is both R and X are doubled and interchanged then,2X/2R is X/R. So the new balance point will be ...